Properties

Label 1140.2.cg
Level $1140$
Weight $2$
Character orbit 1140.cg
Rep. character $\chi_{1140}(131,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.cg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

Total New Old
Modular forms 1488 960 528
Cusp forms 1392 960 432
Eisenstein series 96 0 96

Trace form

\( 960q + 6q^{4} + 12q^{9} + O(q^{10}) \) \( 960q + 6q^{4} + 12q^{9} + 6q^{10} + 24q^{13} - 6q^{16} - 24q^{30} - 12q^{33} - 42q^{34} + 120q^{36} + 186q^{42} + 66q^{48} + 480q^{49} - 48q^{52} - 66q^{54} + 48q^{61} - 42q^{64} + 60q^{66} - 72q^{70} - 84q^{72} + 216q^{73} - 108q^{76} + 60q^{78} - 60q^{81} + 96q^{85} - 48q^{88} - 54q^{90} - 24q^{94} - 252q^{96} + 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)